Seminar Algebra and Geometry: Christian Urech (Universität Basel)

On Cremona Representations

The Cremona group Cr_n of dimension n is the group of birational transformations of projective n-space. It is interesting to study group homomorphisms from Cr_n to Cr_m. However, at the moment it seems to be very difficult to find a general classification.

In this talk I will recall some properties of Cr₂ and define what an algebraic homomorphism between Cremona groups is. Then we will discuss in detail an example given by Gizatullin of an embedding of Cr₂ to Cr₅ and some of its rich geometrical properties.

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